An iterative decomposition method for scatterer reconstruction in R3

In this paper we investigate an iterative method to reconstruct the unknown scatter in R 3 , with only the far-field pattern for just one incident wave. We introduce a general boundary condition and prove its Frechet derivative. Then this iterative method is able to implement without the boundary condition of the scatterer provided. In practical, one can obtain a better reconstruction without a forward solver at each step. The numerical experiments show the feasibility of this method.

[1]  Rainer Kress,et al.  A hybrid method for sound-hard obstacle reconstruction , 2007 .

[2]  Per Christian Hansen,et al.  Regularization Tools version 4.0 for Matlab 7.3 , 2007, Numerical Algorithms.

[3]  Roland Potthast,et al.  A survey on sampling and probe methods for inverse problems , 2006 .

[4]  Pedro Serranho,et al.  A hybrid method for inverse scattering for shape and impedance , 2006 .

[5]  Roland Potthast,et al.  The No Response Test---A Sampling Method for Inverse Scattering Problems , 2003, SIAM J. Appl. Math..

[6]  G. C. Hsiao,et al.  Properties of far‐field operators in acoustic scattering , 1989 .

[7]  Ivan G. Graham,et al.  A high-order algorithm for obstacle scattering in three dimensions , 2004 .

[8]  Rainer Kress,et al.  Newton’s method for inverse obstacle scattering meets the method of least squares , 2003 .

[9]  Haibing Wang,et al.  Some Reconstruction Methods for Inverse Scattering Problems , 2010 .

[10]  Rainer Kress,et al.  Uniqueness and numerical methods in inverse obstacle scattering , 2007 .

[11]  Roland Potthast,et al.  A Survey on Inverse Problems for Applied Sciences , 2013 .

[12]  R. Pinnau,et al.  Regularized fixed-point iterations for nonlinear inverse problems , 2006 .

[13]  Pedro Serranho,et al.  A hybrid method for inverse scattering for Sound-soft obstacles in R3 , 2007 .

[14]  R. Kress,et al.  Integral equation methods in scattering theory , 1983 .

[15]  P. Hansen,et al.  Exploiting Residual Information in the Parameter Choice for Discrete Ill-Posed Problems , 2006 .

[16]  Roland Potthast,et al.  A 'range test' for determining scatterers with unknown physical properties , 2003 .

[17]  R. Kress,et al.  Inverse Acoustic and Electromagnetic Scattering Theory , 1992 .

[18]  Pedro Miguel,et al.  A Hybrid Method for Inverse Obstacle Scattering Problems , 2007 .